The Hyperbolic Formal Affine Demazure Algebra

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• 作者：Marc-Antoine Leclerc
• 关键词：Kac ; Moody algebra ; Hecke algebra ; Formal group law ; Oriented cohomology
• 刊名：Algebras and Representation Theory
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：19
• 期：5
• 页码：1043-1057
• 全文大小：328 KB
• 刊物主题：Commutative Rings and Algebras; Associative Rings and Algebras; Non-associative Rings and Algebras;
• 出版者：Springer Netherlands
• ISSN：1572-9079
• 卷排序：19

文摘

In the present paper we extend the construction of the formal (affine) Demazure algebra due to Hoffnung, Malagón-López, Savage and Zainoulline in two directions. First, we introduce and study the notion of a formal Demazure lattice in the Kac-Moody setting and show that all the definitions and properties of the formal (affine) Demazure operators and algebras hold for such lattices. Second, we show that for the hyperbolic formal group law the formal Demazure algebra is isomorphic (after extending the coefficients) to the Hecke algebra.